David A. Edwards

University of Delaware, Ньюарк, Delaware, United States

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Publications (77)220.18 Total impact

  • Matthew E Zumbrum · David A Edwards
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    ABSTRACT: Optical biosensors are devices used to investigate surface-volume reaction kinetics. Current mathematical models for reaction dynamics rely on the assumption of unidirectional flow within these devices. However, new devices, such as the Flexchip, include a geometry that introduces two-dimensional flow, complicating the depletion of the volume reactant. To account for this, a previous mathematical model is extended to include two-dimensional flow, and the Schwarz-Christoffel mapping is used to relate the physical device geometry to that for a device with unidirectional flow. Mappings for several Flexchip dimensions are considered, and the ligand depletion effect is investigated for one of these mappings. Estimated rate constants are produced for simulated data to quantify the inclusion of two-dimensional flow in the mathematical model.
    No preview · Article · Sep 2014 · Journal of Mathematical Biology
  • Matthew E Zumbrum · David A Edwards
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    ABSTRACT: We analyze surface-volume reactions in the context of optical biosensors with arrays of reacting zones. For arrays having zones with the same rate constants, we consider a two-dimensional reacting zone boundary definition and quantify ligand depletion with the effective Damköhler number. We use asymptotics to obtain ligand depletion results for the one-dimensional case, and also compute results for the circular reacting zone case. For arrays having zones with different rate constants, depletion effects cannot be expressed as the product of time-dependent and space-dependent terms, and we propose two effective rate constant equations for this case.
    No preview · Article · Jul 2014 · Bulletin of Mathematical Biology
  • David A. Edwards
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    ABSTRACT: One technique to study electrochemical oxidation phenomena in thin polymer films is the generation of electrogenerated chemiluminescence (ECL) waves. Such waves are sharp and easy to image, and recent experiments have shown both constant-speed and Fickian-style wave behavior. One way to model such waves mathematically is to track the concentration of the ion clusters in the polymer film. One such model has a standard Fickian form but with a highly nonlinear diffusion coefficient. This model is analyzed numerically, and the results are compared with previous asymptotic analysis. The results demonstrate that ECL waves corresponding to this model are indeed sharp and move in a Fickian way. Hence more complicated effects must be included in the model if constant-speed behavior is to be observed.
    No preview · Article · Mar 2013 · The Journal of Physical Chemistry C
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    ABSTRACT: In order to overcome loss in optical fibers, experimentalists are interested in employing parametric amplifiers using four-wave mixing. Upon linearizing the nonlinear Schrödinger equation typically used as a model for such amplifiers, a system of ODEs results for the complex amplitude. The solution can also be expressed as the product of transfer matrices and the initial condition and its conjugate. Physical insight about the fiber-optic system can be gained by examining the theoretical properties of the matrices in the mathematical system. This module, suitable for inclusion in an advanced undergraduate or graduate linear algebra course, explores these properties and should provide a good physical motivation for the theoretical explorations in such a course.
    No preview · Article · Jan 2013 · SIAM Review
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    ABSTRACT: Injectable biomaterials are increasingly being explored to minimize risks and complications associated with surgical implantation. We describe a strategy for delivery via conventional needle-syringe injection of large preformed macroporous scaffolds with well-defined properties. Injectable 3D scaffolds, in the form of elastic sponge-like matrices, were prepared by environmentally friendly cryotropic gelation of a naturally sourced polymer. Cryogels with shape-memory properties may be molded to a variety of shapes and sizes, and may be optionally loaded with therapeutic agents or cells. These scaffolds have the capability to withstand reversible deformations at over 90% strain level, and a rapid volumetric recovery allows the structurally defined scaffolds to be injected through a small-bore needle with nearly complete geometric restoration once delivered. These gels demonstrated long-term release of biomolecules in vivo. Furthermore, cryogels impregnated with bioluminescent reporter cells provided enhanced survival, higher local retention, and extended engraftment of transplanted cells at the injection site compared with a standard injection technique. These injectable scaffolds show great promise for various biomedical applications, including cell therapies.
    Full-text · Article · Nov 2012 · Proceedings of the National Academy of Sciences
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    Dejun Xie · David A. Edwards · Gilberto Schleiniger · Qinghua Zhu
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    ABSTRACT: Understanding the behaviour of the American put option is one of the classic problems in mathematical finance. Considerable efforts have been made to understand the asymptotic expansion of the optimal early exercise boundary for small time near expiry. Here we focus on the large-time expansion of the boundary. Based on a recent development of the convexity property, we are able to establish two integral identities pertaining to the boundary, from which the upper bound of its large-time expansion is derived. The bound includes parameter dependence in the exponential decay to its limiting value. In addition, these time explicit identities provide very efficient numerical approximations to the true solution to the problem.
    Preview · Article · Sep 2011 · Applied Mathematical Finance
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    David A Edwards
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    ABSTRACT: The ubiquity of surface-volume reactions in biological and industrial processes makes knowledge of their kinetics critical. This has spurred technological advances in several biosensors designed to measure rate constants, such as the Flexchip and the dotLab. These biosensors have multiple reacting zones in a single flow channel, and hence they also serve as good model systems for biochemical systems with multiple reacting zones, such as cell membranes. A correct mathematical model for such systems must incorporate the effects of transport and zone position. A basic unidirectional flow model is developed in general and solved for typical experimental parameters using perturbation methods. The effect of zone placement along the channel can be quantified in terms of an effective Damköhler number based upon position. Moreover, it is established that zone placement across the channel does not affect the measurements.
    Preview · Article · Mar 2011 · Mathematical biosciences
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    Full-text · Article · Feb 2011 · Medecine sciences: M/S
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    ABSTRACT: This study establishes the immune response elicited in guinea pigs after pulmonary and parenteral immunizations with diphtheria CRM-197 antigen (CrmAg). Several spray-dried powders of formalin-treated/untreated CrmAg nanoaggregates with L-leucine were delivered to the lungs of guinea pigs. A control group consisting of alum with adsorbed CrmAg in saline was administered by intramuscular injection. Animals received three doses of powder vaccines containing 20 or 40 μg of CrmAg. The serum IgG titers were measured for 16 weeks after the initial immunization; IgA titers were measured at the time of sacrifice in the broncho-alveolar lavage fluid. Further, toxin neutralization tests in naïve guinea pigs were performed for a few select serum samples. Histopathology of the lung tissues was conducted to evaluate inflammation or injury to the lung tissues. While the highest titer of serum IgG antibody was observed in guinea pigs immunized by the intramuscular route, those animals immunized with dry powder formulation by the pulmonary route, and without the adjuvant alum, exhibited high IgA titers. A pulmonary administered dry powder, compared to parenteral immunization, conferred complete protection in the toxin neutralization test. Mild inflammation was observed in lung tissues of animals receiving dry powder vaccines by the pulmonary route. Thus, administering novel CrmAg as dry powders to the lungs may be able to overcome some of the disadvantages observed with the existing diphtheria vaccine which is administered by the parenteral route. In addition, these powders will have the advantage of eliciting a high mucosal immune response in the lungs without using traditional adjuvants.
    Full-text · Article · Sep 2010 · The AAPS Journal
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    ABSTRACT: To extend the retention time of aerosol-delivered growth factors in the lung for stem cell homing/activation purposes, we examined a formulation of vascular endothelial growth factor (VEGF) complexed to dextran sulfate (DS) and chitosan (CS) polyelectrolytes. Optimal incorporation of VEGF was found at a VEGF/DS/CS ratio of 0.12:1:0.33, which resulted in nanoparticle complexes with diameters of 612+/-79 nm and zeta potentials of -31+/-1 mV. The complexes collapsed in physiological solution, and released VEGF in a biphasic time course in vitro. In rat lungs, however, VEGF delivered in the complex was cleared at a constant exponential decay rate, 8-fold slower than that delivered in free form. The extended VEGF retention was likely due to equilibrium binding of VEGF to DS and to endogenous glycosaminoglycans. A similar retention effect is expected with other glycosaminoglycans-binding proteins (including many growth factors) when complexed with these glycans. Owing to its unique application, this type of complex is, perhaps, better described as a nanoglycan complex.
    Preview · Article · Jul 2010 · Biomacromolecules
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    ABSTRACT: Novel treatments for multidrug-resistant tuberculosis (MDR-TB), extensively drug-resistant tuberculosis (XDR-TB), or latent TB are needed urgently. Recently, we reported the formulation and characterization of the nitroimidazo-oxazine PA-824 for efficient aerosol delivery as dry powder porous particles and the subsequent disposition in guinea pigs after pulmonary administration. The objective of the present study was to evaluate the effects of these PA-824 therapeutic aerosols on the extent of TB infection in the low-inoculum aerosol infection guinea pig model. Four weeks after infection by the pulmonary route, animals received daily treatment for 4 weeks of either a high or a low dose of PA-824 dry powder aerosol. Animals received PA-824 cyclodextrin/lecithin suspensions orally as positive controls, and those receiving placebo particles or no treatment were negative controls. The lungs and spleens of animals receiving the high dose of inhaled PA-824 particles exhibited a lower degree of inflammation (indicated by wet tissue weights), bacterial burden, and tissue damage (indicated by histopathology) than those of untreated or placebo animals. Treatment with oral PA-824 cyclodextrin/lecithin suspension resulted in a more significant reduction in the bacterial burden of lungs and spleen, consistent with a dose that was larger than inhaled doses (eight times the inhaled low dose and four times the inhaled high dose). However, histopathological analysis revealed that the extent of tissue damage was comparable in groups receiving the oral or either inhaled dose. The present studies indicate the potential use of PA-824 dry powder aerosols in the treatment of TB.
    Full-text · Article · Apr 2010 · Antimicrobial Agents and Chemotherapy
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    ABSTRACT: We find that Mycobacterium smegmatis survives spray drying and retains cell viability in accelerated temperature stress (40 °C) conditions with a success rate that increases with increasing thermal, osmotic, and nutrient-restriction stresses applied to the mycobacterium prior to spray drying. M.smegmatis that are spray dried during log growth phase, where they suffer little or no nutrient-reduction stress, survive for less than 7 days in the dry powder state at accelerated temperature stress conditions, whereas M. smegmatis that are spray dried during stationary phase, where cells do suffer nutrient reduction, survive for up to 14 days. M. smegmatis that are spray dried from stationary phase, subjected to accelerated temperature stress conditions, regrown to stationary phase, spray dried again, and resubmitted to this same process four consecutive times, display, on the fourth spray drying iteration, an approximate ten-fold increase in stability during accelerated temperature stress testing, surviving up to 105 days. Microarray tests revealed significant differences in genetic expression of M. smegmatis between log phase and stationary phase conditions, between naïve (non spray-dried) and multiply cycled dried M. smegmatis (in log and stationary phase), and between M. smegmatis in the dry powder state following a single spray drying operation and after four consecutive spray drying operations. These differences, and other phenotypical differences, point to the carotenoid biosynthetic pathway as a probable pathway contributing to bacteria survival in the spray-dried state and suggests strategies for spray drying that may lead to significantly greater room-temperature stability of mycobacteria, including mycobacterium bovis bacille Calmette-Guerin (BCG), the current TB vaccine.
    Preview · Article · Apr 2010 · Materials
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    Ying Liu · Jean Sung · Robert K Prud 'homme · David A Edwards

    Full-text · Article · Jan 2010
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    ABSTRACT: The lens capsule compartmentalizes the cells of the avascular lens from other ocular tissues. Small molecules required for lens cell metabolism, such as glucose, salts, and waste products, freely pass through the capsule. However, the lens capsule is selectively permeable to proteins such as growth hormones and substrate carriers which are required for proper lens growth and development. We used fluorescence recovery after photobleaching (FRAP) to characterize the diffusional behavior of various sized dextrans (3, 10, 40, 150, and 250 kDa) and proteins endogenous to the lens environment (EGF, gammaD-crystallin, BSA, transferrin, ceruloplasmin, and IgG) within the capsules of whole living lenses. We found that proteins had dramatically different diffusion and partition coefficients as well as capsule matrix binding affinities than similar sized dextrans, but they had comparable permeabilities. We also found ionic interactions between proteins and the capsule matrix significantly influence permeability and binding affinity, while hydrophobic interactions had less of an effect. The removal of a single anionic residue from the surface of a protein, gammaD-crystallin [E107A], significantly altered its permeability and matrix binding affinity in the capsule. Our data indicated that permeabilities and binding affinities in the lens capsule varied between individual proteins and cannot be predicted by isoelectric points or molecular size alone.
    Full-text · Article · Dec 2009 · Matrix biology: journal of the International Society for Matrix Biology
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    ABSTRACT: To formulate rifampicin, an anti-tuberculosis antibiotic, for aerosol delivery in a dry powder 'porous nanoparticle-aggregate particle' (PNAP) form suited for shelf stability, effective dispersibility and extended release with local lung and systemic drug delivery. Rifampicin was encapsulated in PLGA nanoparticles by a solvent evaporation process, spray dried into PNAPs containing varying amounts of nanoparticles, and characterized for physical and aerosol properties. Pharmacokinetic studies were performed with formulations delivered to guinea pigs by intratracheal insufflation and compared to oral and intravenous delivery of rifampicin. The PNAP formulations possessed properties suitable for efficient deposition in the lungs. In vitro release showed an initial burst of rifampicin, with the remainder available for release beyond eight hours. PNAPs delivered to guinea pigs by insufflation achieved systemic levels of rifampicin detected for six to eight hours. Moreover, rifampicin concentrations remained detectable in lung tissue and cells up to and beyond eight hours. Conversely, after pulmonary delivery of an aerosol without nanoparticles, rifampicin could not be detected in the lungs at eight hours. Our results indicate that rifampicin can be formulated into an aggregated nanoparticle form that, once delivered to animals, achieves systemic exposure and extends levels of drug in the lungs.
    Full-text · Article · May 2009 · Pharmaceutical Research
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    ABSTRACT: We formulated PA-824, a nitroimidazopyran with promise for the treatment of tuberculosis, for efficient aerosol delivery to the lungs in a dry powder porous particle form. The objectives of this study were to prepare and characterize a particulate form of PA-824, assess the stability of this aerosol formulation under different environmental conditions, and determine the pharmacokinetic parameters for the powder after pulmonary administration. The drug was spray dried into porous particles containing a high drug load and possessing desirable aerosol properties for efficient deposition in the lungs. The physical, aerodynamic, and chemical properties of the dry powder were stable at room temperature for 6 months and under refrigerated conditions for at least 1 year. Pharmacokinetic parameters were determined in guinea pigs after the pulmonary administration of the PA-824 powder formulation at three doses (20, 40, and 60 mg/kg of body weight) and compared to those after the intravenous (20 mg/kg) and oral (40 mg/kg) delivery of the drug. Oral and inhaled delivery of PA-824 achieved equivalent systemic delivery at the same body dose within the first 12 h of dosing. However, animals dosed by the pulmonary route showed drug loads that remained locally in the lungs for 32 h postexposure, whereas those given the drug orally cleared the drug more rapidly. Therefore, we expect from these pharmacokinetic data that pulmonary delivery may achieve the same efficacy as oral delivery at the same body dose, with a potential improvement in efficacy related to pulmonary infection. This may translate into the ability to deliver lower body doses of this drug for the treatment of tuberculosis by aerosol.
    Full-text · Article · Feb 2009 · Antimicrobial Agents and Chemotherapy
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    ABSTRACT: Identification of detailed features of neuronal systems is an important challenge in the biosciences today. Transduction of an odor into an electrical signal occurs in the membranes of the cilia. The Cl(Ca) channels that reside in the ciliary membrane are activated by calcium, allow a depolarizing efflux of Cl− and are thought to amplify the electrical signal to the brain. In this paper, a mathematical model consisting of partial differential equations is developed to study two different experiments; one involving the interaction of the cyclic-nucleotide-gated (CNG) and Cl(Ca) channels and the other, the diffusion of Ca2+ into cilia. This work builds on an earlier study (Mathematical modeling of the Cl(Ca) ion channels in frog olfactory cilia. Ph.D. Thesis, University of Cincinnati, Cincinnati, OH, 2006; Math. Comput. Modelling 2006; 43:945–956; Biophys. J. 2006; 91:179–188), which suggested that the CNG channels are clustered at about 0.28 of the length of a cilium from its open end. Closed-form solutions are derived after certain reductions in the model are made. These special solutions provide estimates of the channel distributions. Scientific computation is also used. This preliminary study suggests that the Cl(Ca) ion channels are also clustered at about one-third of the length of a cilium from its open end. Copyright
    Preview · Article · Oct 2008 · Mathematical Methods in the Applied Sciences
  • Jean C Sung · Brian L Pulliam · David A Edwards
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    ABSTRACT: The lungs are an attractive route for non-invasive drug delivery with advantages for both systemic and local applications. Incorporating therapeutics with polymeric nanoparticles offers additional degrees of manipulation for delivery systems, providing sustained release and the ability to target specific cells and organs. However, nanoparticle delivery to the lungs has many challenges including formulation instability due to particle-particle interactions and poor delivery efficiency due to exhalation of low-inertia nanoparticles. Thus, novel methods formulating nanoparticles into the form of micron-scale dry powders have been developed. These carrier particles exhibit improved handling and delivery, while releasing nanoparticles upon deposition in the lungs. This review covers the development of nanoparticle formulations for pulmonary delivery as both individual nanoparticles and encapsulated within carrier particles.
    No preview · Article · Jan 2008 · Trends in Biotechnology
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    Donald A French · David A Edwards
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    ABSTRACT: In this paper, a mathematical model of the diffusion of cAMP into olfactory cilia and the resulting electrical activity is presented. The model, which consists of two nonlinear differential equations, is studied using perturbation techniques. The unknowns in the problem are the concentration of cAMP, the membrane potential, and the quantity of most interest in this work: the distribution of CNG channels along the length of a cilium. Experimental measurements of the total current during this diffusion process provide an extra boundary condition which helps determine the unknown distribution function. A simple perturbation approximation is derived and used to solve this inverse problem and thus obtain estimates of the spatial distribution of CNG ion channels along the length of a cilium. A one-dimensional computer minimization and a special delay iteration are used with the perturbation formulas to obtain approximate channel distributions in the cases of simulated and experimental data.
    Preview · Article · Dec 2007 · Journal of Mathematical Biology
  • Brian Pulliam · Jean C Sung · David A Edwards
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    ABSTRACT: The development of needle-less vaccination for pulmonary delivery may require dry forms of vaccines whose powder properties allow for a low cost, heat and freeze tolerance, efficient aerosolization, and the ability to target cells of the immune system. For each of these reasons, nanoparticles can play a critical role in the formulation, development and delivery of needle-less vaccination. This review aims to communicate present biomaterial design issues surrounding the incorporation of nanoparticles into pulmonary vaccines.
    No preview · Article · Dec 2007 · Expert Opinion on Drug Delivery

Publication Stats

3k Citations
220.18 Total Impact Points


  • 1999-2014
    • University of Delaware
      • Department of Mathematical Sciences
      Ньюарк, Delaware, United States
  • 2002-2012
    • Harvard University
      • School of Engineering and Applied Sciences
      Cambridge, Massachusetts, United States
  • 2010
    • Princeton University
      • Department of Chemical and Biological Engineering
      Princeton, New Jersey, United States
  • 2007-2010
    • Harvard School of Engineering and Applied Sciences
      Londinium, England, United Kingdom
  • 1996-2000
    • Pennsylvania State University
      • Department of Chemical Engineering
      University Park, Maryland, United States
  • 1997-1999
    • University of Maryland, College Park
      • Department of Mathematics
      College Park, MD, United States
  • 1998
    • University of Alberta
      • Department of Chemical and Materials Engineering
      Edmonton, Alberta, Canada
  • 1997-1998
    • William Penn University
      University Park, Florida, United States
  • 1995
    • CUNY Graduate Center
      New York, New York, United States
    • California Institute of Technology
      Pasadena, California, United States
  • 1993-1995
    • Massachusetts Institute of Technology
      • Department of Chemical Engineering
      Cambridge, Massachusetts, United States